{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# Physics 3: Blackhole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "a0b181a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from kan import *\n",
    "from kan.utils import batch_jacobian\n",
    "from kan.MLP import MLP\n",
    "\n",
    "torch.use_deterministic_algorithms(True)\n",
    "torch.set_default_dtype(torch.float64)\n",
    "\n",
    "#model = KAN(width=[1,5,5,1], grid=5, grid_range=[1.2,3], grid_eps=0.)\n",
    "#model = KAN(width=[1,1], grid=1, grid_range=[1.2,3], grid_eps=0., base_fun='zero')\n",
    "#model.speed()\n",
    "model = MLP(width=[1,20,20,1])\n",
    "\n",
    "#model = lambda x: 2 * torch.sqrt(x) + torch.log((torch.sqrt(x)-1)/(torch.sqrt(x)+1))\n",
    "\n",
    "# Schwarzschild 2M = 1\n",
    "def g(x_):\n",
    "    bs = x_.shape[0]\n",
    "    t = x_[:,0]\n",
    "    a = torch.ones_like(t)\n",
    "    x = x_[:,1]\n",
    "    y = x_[:,2]\n",
    "    z = x_[:,3]\n",
    "    r = torch.sqrt(x**2+y**2+z**2)\n",
    "    stack1 = torch.stack([torch.ones(bs,)-1/r, torch.zeros(bs,), torch.zeros(bs,), torch.zeros(bs,)])\n",
    "    stack2 = torch.stack([torch.zeros(bs,), -(1+x**2/((r-1)*r**2)), -x*y/((r-1)*r**2), -x*z/((r-1)*r**2)])\n",
    "    stack3 = torch.stack([torch.zeros(bs,), -x*y/((r-1)*r**2), -(1+y**2/((r-1)*r**2)), -y*z/((r-1)*r**2)])\n",
    "    stack4 = torch.stack([torch.zeros(bs,), -x*z/((r-1)*r**2), -y*z/((r-1)*r**2), -(1+z**2/((r-1)*r**2))])\n",
    "    gs = torch.stack([stack1, stack2, stack3, stack4]).permute(2,0,1)\n",
    "    return gs\n",
    "\n",
    "def transform_g(transform, g, x):\n",
    "    jac = batch_jacobian(transform, x, create_graph=True, mode='vector')\n",
    "    jac_inv = torch.inverse(jac)\n",
    "    return torch.matmul(torch.matmul(jac_inv.permute(0,2,1), g(x)),jac_inv)\n",
    "\n",
    "def transform(x):\n",
    "    t = x[:,[0]]\n",
    "    r = torch.linalg.norm(x[:,1:], dim=1, keepdim=True)\n",
    "    tp = t + model(r)\n",
    "    #u = torch.sqrt(r)\n",
    "    #tp = t - (2*u+torch.log((u-1)/(u+1)))\n",
    "    return torch.cat([tp, x[:,1:]], dim=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "25cc9ac5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| loss: 1.05e-04 |: 100%|█████████████████████████████████████████████| 5/5 [00:12<00:00,  2.42s/it]\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "from kan.utils import batch_jacobian, create_dataset_from_data\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "steps = 5\n",
    "log = 1\n",
    "optimizer = LBFGS(model.parameters(), lr=1, history_size=10, line_search_fn=\"strong_wolfe\", tolerance_grad=1e-32, tolerance_change=1e-32, tolerance_ys=1e-32)\n",
    "#optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)\n",
    "#optimizer = torch.optim.Adam([], lr=1e-3)\n",
    "pbar = tqdm(range(steps), desc='description', ncols=100)\n",
    "\n",
    "n_train = 10000\n",
    "W = torch.normal(0,1,size=(n_train,4))\n",
    "input_ = torch.empty(n_train,4, requires_grad=False)\n",
    "input_[:,0] = torch.rand(n_train, requires_grad=True)\n",
    "#rs = 1.2 + 1.8 * torch.linspace(0,1,n_train)\n",
    "rs = 1.2 + 1.8 * torch.linspace(0,1,n_train)\n",
    "input_[:,1:] = W[:,1:]/torch.norm(W[:,1:], dim=1, keepdim=True)*torch.unsqueeze(rs, dim=1)\n",
    "x = input_.detach().requires_grad_(True)\n",
    "\n",
    "def closure():\n",
    "    \n",
    "    global loss\n",
    "    global x\n",
    "    optimizer.zero_grad()\n",
    "    \n",
    "    g_GP = transform_g(transform, g, x)\n",
    "    num = x.shape[0]\n",
    "    loss = torch.mean((g_GP[:,1:,1:] + torch.eye(3,3)[None,:,:].expand(num,3,3))**2)\n",
    "\n",
    "    loss.backward()\n",
    "    return loss\n",
    "\n",
    "for _ in pbar:\n",
    "        \n",
    "    '''if _ < 50 and _ % 5 == 0:\n",
    "        model.update_grid(x)'''\n",
    "        \n",
    "    optimizer.step(closure)\n",
    "    \n",
    "    if _ % log == 0:\n",
    "        pbar.set_description(\"| loss: %.2e |\" % loss.cpu().detach().numpy())\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "72338f98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    }
   ],
   "source": [
    "model = model.refine(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56097cdf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "8f69f79a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(1.5, -23.3, '$-(2\\\\sqrt{r}+{\\\\rm log}(\\\\frac{\\\\sqrt{r}-1}{\\\\sqrt{r}+1}))+C$')"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(rs.detach().numpy(), model(rs[:,None])[:,0].detach().numpy())\n",
    "u = torch.sqrt(rs)\n",
    "dt = 2*u + torch.log((u-1)/(u+1))\n",
    "#plt.plot(rs, dt+3.65, color='red', ls='--', lw=2)\n",
    "plt.plot(rs, -dt-23.85, color='orange', ls='--', lw=2)\n",
    "plt.xlabel(r'$r$', fontsize=20)\n",
    "plt.ylabel(r'$\\Delta t$', fontsize=20)\n",
    "#plt.text(1.5,3,r'$2\\sqrt{r}+{\\rm log}(\\frac{\\sqrt{r}-1}{\\sqrt{r}+1})+C_1$',color='red',fontsize=20)\n",
    "plt.text(1.5,-23.3,r'$-(2\\sqrt{r}+{\\rm log}(\\frac{\\sqrt{r}-1}{\\sqrt{r}+1}))+C$',color='orange',fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "0ae68116",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(1.5, 7, '$-(2\\\\sqrt{r}+{\\\\rm log}(\\\\frac{\\\\sqrt{r}-1}{\\\\sqrt{r}+1}))+C_2$')"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(rs.detach().numpy(), model(rs[:,None])[:,0].detach().numpy())\n",
    "u = torch.sqrt(rs)\n",
    "dt = 2*u + torch.log((u-1)/(u+1))\n",
    "plt.plot(rs, dt+3.65, color='red', ls='--', lw=2)\n",
    "plt.plot(rs, -dt+6.5, color='orange', ls='--', lw=2)\n",
    "plt.xlabel(r'$r$', fontsize=20)\n",
    "plt.ylabel(r'$\\Delta t$', fontsize=20)\n",
    "plt.text(1.5,3,r'$2\\sqrt{r}+{\\rm log}(\\frac{\\sqrt{r}-1}{\\sqrt{r}+1})+C_1$',color='red',fontsize=20)\n",
    "plt.text(1.5,7,r'$-(2\\sqrt{r}+{\\rm log}(\\frac{\\sqrt{r}-1}{\\sqrt{r}+1}))+C_2$',color='orange',fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "351b8e15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7ff4489537f0>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(rs.detach().numpy(), model(rs[:,None])[:,0].detach().numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "46b2c8ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "g_GP = transform_g(transform, g, x)\n",
    "num = x.shape[0]\n",
    "loss = torch.mean((g_GP[:,1:,1:] + torch.eye(3,3)[None,:,:].expand(num,3,3))**2, dim=[1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "94dbeda7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.4633e-03, 2.4056e-03, 2.3489e-03,  ..., 5.6274e-05, 5.7003e-05,\n",
       "        5.7739e-05], grad_fn=<MeanBackward1>)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "9f2aa78a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ff41eb709a0>]"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rs.detach().numpy(), loss.detach().numpy())\n",
    "plt.xlabel(r'$r$', fontsize=20)\n",
    "plt.ylabel('Minkowski Loss', fontsize=20)\n",
    "plt.plot([2.282,2.282],[0,0.08], ls='--', color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9188b3ed",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
